Your first step in both cases is RNA isolation. You can split the RNA sample after isolation. You need to do an RNA isolation which preserves the small miRNA fragments. This probably is an acidic phenol or Trizol isolation.

Thanks. I thought about this solution, but I just couldn't be sure whether the amount of RNA will be enough for both processes.

How about splitting cells after silencing process? It doesn't sound scientific, though. But maybe we can use one half of the cells for the confirmation of silencing and the other for miRNA analysis. My concern is that can we make sure that the cells we are gonna use for miRNA isolation are X gene-silenced?